Question

An elevator with a total mass of 1000 kg is supported by a cable with a tension force of 15,000 N. What is the magnitude and direction of the elevator's acceleration under the influence of gravity (approximately 9.8 m/s²)?

A) Acceleration is 4.2 m/s² upward.
B) Acceleration is 4.2 m/s² downward.
C) Acceleration is 9.8 m/s² upward.
D) Acceleration is 9.8 m/s² downward.

Answer 1

The elevator's acceleration is 5.2 m/s² upward, which is determined by using Newton's second law and considering the net force acting on the elevator after subtracting the gravitational force from the tension force.

Step-by-step explanation:

The magnitude and direction of the elevator's acceleration can be calculated using Newton's second law, which states that the net force acting on an object is equal to the product of the object's mass and its acceleration (F=ma). The tension force in the cable (15,000 N) is acting upwards, while the weight of the elevator (gravity force), which can be calculated as mass times the acceleration due to gravity (1000 kg × 9.8 m/s² = 9,800 N), acts downwards.

To find the net force, we subtract the gravitational force from the tension force: Net Force = Tension - Weight = 15,000 N - 9,800 N = 5,200 N.

The acceleration of the elevator can then be found by dividing the net force by the mass of the elevator: Acceleration = Net Force / Mass = 5,200 N / 1000 kg = 5.2 m/s². Since the tension is greater than the weight, the acceleration is upward.